Shopify, Lulu Direct, and Amazon

Hi,

I am looking to create a journal to sell. After looking at options, the only place I can find print on demand for what I want is Lulu direct. They will only link with Shopify. And I know Shopify can link with Amazon. So my question is, is it possible to basically link all three in a chain? For instance, if someone ordered on Amazon and it went through Shopify, would that be able to have Lulu direct print it like they would if it was a sale directly from Shopify? I want to sell on Amazon, but their own POD services aren't sufficient for the project I have in mind.